Taxi from JFK to hotel will cost $45+tolls+tip. Taxi to LGA from hotel is about $30+tolls+tip. NYAS runs shuttle buses to/from both airports to Grand Central Station which is only a few blocks from your hotel; cost from JFK is $15, to LGA is $12. Public transportation (subway, LIRR) is easily accessible from JFK via Airtrain LGA is not, best to take a taxi there.
Taxi from JFK to hotel will